Birational geometry of the moduli space of pure sheaves on quadric surface

Kiryong Chung; Han-Bom Moon

doi:10.1016/j.crma.2017.09.005

Algebraic geometry

Birational geometry of the moduli space of pure sheaves on quadric surface

Presented by: Claire Voisin

Kiryong Chung ¹; Han-Bom Moon ²

¹ Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
² School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States

Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1082-1088.

Abstract
Résumé

We study birational geometry of the moduli space of stable sheaves on a quadric surface with Hilbert polynomial $5 m + 1$ and $c_{1} = (2, 3)$ . We describe a birational map between the moduli space and a projective bundle over a Grassmannian as a composition of smooth blow-ups/downs.

Dans cette note, nous étudions la géométrie birationnelle de l'espace des modules des faisceaux stables sur une quadrique, de polynôme de Hilbert $5 m + 1$ et de classes de Chern $(2, 3)$ . Pour cela, nous donnons une application birationnelle entre l'espace des modules et un fibré projectif au dessus d'une grassmanienne, qui est une composition d'éclatements et de contractions lisses.

Received: 2017-03-10
Accepted: 2017-09-01
Published online: 2017-09-20

DOI: 10.1016/j.crma.2017.09.005

Author's affiliations:

Kiryong Chung ¹; Han-Bom Moon ²

¹ Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
² School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States

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     author = {Kiryong Chung and Han-Bom Moon},
     title = {Birational geometry of the moduli space of pure sheaves on quadric surface},
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     number = {10},
     year = {2017},
     doi = {10.1016/j.crma.2017.09.005},
     language = {en},
}

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Kiryong Chung; Han-Bom Moon. Birational geometry of the moduli space of pure sheaves on quadric surface. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1082-1088. doi : 10.1016/j.crma.2017.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.005/

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